Error Bars for Lua Maths in Warcraft 3

[KirinXP]

Hi.

I was testing some Lua maths in Warcraft 3 involving quadratic and apparently the obtained numerical value differs depending on whether math.sqrt or "^(1/2)" is used. Mathematically, they should be equivalent, thus, the same answer should yield. However, there seem to be a large difference in accuracy depending on which one of them is used.

Spoiler: Calculation Using math.sqrt

So the computed answer deviated approximately 2.2e-5 to 2.3e-5 from the real answer.

function maths()
    a = -1
    b = -4
    c = 7
    do
        local a2 = 2*a
        local d = math.sqrt(b^2 - 4*a*c)
        print("The value of d is "..d)
        x1 = (-b + d)/a2
        x2 = (-b - d)/a2
    end
    print("The roots are"..x1.." and "..x2)
    ans1 = -5.31662479 --The answers that should be obtained
    ans2 = 1.31662479
    D1 = math.abs(ans1 - x1)
    D2 = math.abs(ans2 -x2)
    print("The differences are "..D1.." and "..D2)
end

Spoiler: Calculation Using "^(1/2)"

Now the computed answer deviated approximately 1.4e-6 to 1.5e-6 from the real answer.

function maths()
    a = -1
    b = -4
    c = 7
    do
        local a2 = 2*a
        local d = (b^2 - 4*a*c)^(1/2) -- Note that ^(1/2) is now used instead of math.sqrt
        print("The value of d is "..d)
        x1 = (-b + d)/a2
        x2 = (-b - d)/a2
    end
    print("The roots are"..x1.." and "..x2)
    ans1 = -5.31662479 --The answers that should be obtained
    ans2 = 1.31662479
    D1 = math.abs(ans1 - x1)
    D2 = math.abs(ans2 -x2)
    print("The differences are "..D1.." and "..D2)
end

There is no deviation from the true answer at all when both computation method are utilised in Lua but when it is used in Warcraft 3 Worldeditor it yields different results. Although a deviation of e-5 or e-6 shouldn't dramatically affect any coding that requires sqrt but it is just interesting how different results yield.

Edit: I guess it is just some floating point error issue and that two methods are considered different in war3.